Activity Budget Analysis
Cali Wilson
5/20/2022
How does urbanization influence ibis behaviors relevant to transmission?
Specifically, how does variation in flock size and frequency of provisioning influence these behaviors?
Data:
10-minute focal follow observations of birds at 5 urban parks in South Florida. Follows conducted during summer 2019.
Focal follows were only conducted in urban parks
Note: Focal follows were only conducted when people were not actively feeding the birds so foraging means probing on the ground for food. The few instances of consuming human provided food are cases where ibis were foraging ‘naturally’ and happened upon scraps of anthropogenic food that was already on the ground.
Sample Sizes / Data Structure
Observations consist of 168 focal follows lasting > 2 minutes. Five urban parks were samples for ~30 focals per site. Sites were visited 2-4 times each.
Provisioning estimates: Each visit, # of people and groups feeding birds were recorded for duration of visit. Provisioning was estimated by counting the number of groups that fed the birds per visit and dividing by total time I was at the site to get # provisioning events/ hour. Each focal follow was paired with the average # of provisioning events per hour on day/site of the focal follow.
Flock size estimates: Every ~30 minutes, flock size was recorded. I paired each focal follow with the nearest estimate of flock size.
Birds seem to spend the most time foraging, grooming, and being vigilant.
I am going to re-group these variables according to their relevance to different modes of parasite transmission (see different sections below).
Summary Statistics
How many focal follows lasted > 2 minutes? *important- when we add in predictors later, we lose data for 3 follows because they lack corresponding predictor data.
## [1] 150What was the total amount of time spent observing ibis? (this only includes obs >2 minutes aka the ones used in the analysis)
Total obs time in seconds:
## [1] 79994Total obs time in minutes:
## [1] 1333.233Mean obs time:
## [1] 533.2933How many different behaviors were observed on average for each ibis during the observation?
## focalID n_behaviors
## Length:150 Min. :2.000
## Class :character 1st Qu.:3.000
## Mode :character Median :4.000
## Mean :3.853
## 3rd Qu.:5.000
## Max. :6.000How many birds showed 2 or more behaviors?
nrow(sum3.1[sum3.1$n_behaviors >= 2,]) #all birds observed for at least 2 minutes did 2 or more behaviors ## [1] 150nrow(sum3.1[sum3.1$n_behaviors < 2,])## [1] 0Most commonly observed behaviors observed?
How many birds foraged?
sum4 <- simp2
sum4f <- subset(sum4, Activity=="Foraging" & activity_count > 0)
summary(sum4f)## focalID focalduration Activity activity_count
## Length:110 Min. :139.0 Length:110 Min. : 4.0
## Class :character 1st Qu.:592.0 Class :character 1st Qu.: 53.5
## Mode :character Median :596.0 Mode :character Median :148.0
## Mean :537.1 Mean :212.6
## 3rd Qu.:597.0 3rd Qu.:362.0
## Max. :598.0 Max. :585.0How many birds groomed?
sum4g <- subset(sum4, Activity=="Grooming" & activity_count > 0)
summary(sum4g)## focalID focalduration Activity activity_count
## Length:113 Min. :122.0 Length:113 Min. : 2.0
## Class :character 1st Qu.:557.0 Class :character 1st Qu.: 22.0
## Mode :character Median :596.0 Mode :character Median :140.0
## Mean :536.5 Mean :170.8
## 3rd Qu.:597.0 3rd Qu.:275.0
## Max. :598.0 Max. :572.0How many birds were vigilant?
sum4v <- subset(sum4, Activity=="Vigilant" & activity_count > 0)
summary(sum4v)## focalID focalduration Activity activity_count
## Length:140 Min. :122.0 Length:140 Min. : 4.00
## Class :character 1st Qu.:579.8 Class :character 1st Qu.: 41.75
## Mode :character Median :596.0 Mode :character Median :132.50
## Mean :539.2 Mean :178.65
## 3rd Qu.:597.0 3rd Qu.:269.00
## Max. :598.0 Max. :591.00What behaviors did ibis spend the most time doing?
sum5<-simp2
sum5 <- sum5 %>% group_by(Activity) %>% summarise(sum(activity_count))
sum5## # A tibble: 7 × 2
## Activity `sum(activity_count)`
## <chr> <dbl>
## 1 Drinking 243
## 2 Foraging 23387
## 3 Grooming 19305
## 4 Other 812
## 5 Resting 2934
## 6 Vigilant 25011
## 7 Walking 8302Which behaviors were observed most frequently in ibis?
sum6<-simp2
sum6<- as.data.frame(subset(simp2, activity_count > 0))
sum6.1 <- sum6 %>% group_by(Activity) %>%
summarise(n_focals=n(),
.groups = 'drop')
sum6.1## # A tibble: 7 × 2
## Activity n_focals
## <chr> <int>
## 1 Drinking 19
## 2 Foraging 110
## 3 Grooming 113
## 4 Other 61
## 5 Resting 20
## 6 Vigilant 140
## 7 Walking 115Visualizations of predictors
Predictors:
- nearest flock size estimate
- feeding events per hour
- site? (not really interested in site-level differences per say but might help us understand if there are other inherent differences across sites that we aren’t currently measuring)
What is the distribution of provisioning frequency? What about average flock size? Do we see any relationship between # feeding events and average flock size?
Note: Here I’m showing avg flock size and nearest flock size
Model visualizations and Model Selection
Water Exposure
This variable includes foraging in water, bathing, and drinking.
Main Q’s:
Does flock size influence behaviors related to the exposure of waterborne pathogens?
Does the amount of human provided food influence behaviors related to the exposure of waterborne pathogens?
Exploratory Visualizations
First, what does the distribution of water exposure look like? Plot water exposure by flock size, provisioning, and site to look for potential trends. (set to ‘show nothing, run code’ so rmd isn’t super long)
Models
Standardize predictor variables
Model selection:
Build a super model and then remove variables in a biologically relevant way to see how fit changes and compare AIC values.
Hypothesis testing approach:
Is flock size important? Is provisioning important?
Model diagnostics
Not yet finished. Code is set to ‘don’t run’ at the moment.
Ectoparasite removal
This variable includes preening and bathing.
(set to ‘show nothing, run code’ so rmd isn’t super long)
Foraging / Preening trade-off
Main Q’s:
Does flock size, provisioning, both, or neither influence foraging time? What about preening time?
Literature suggests potential trade-offs between these behaviors. Would be interesting to see if we see differences in either of them and if so, are the effects opposite each other?
Models
Standardize predictor variables
#library(mosaic) # standardizing variables
ForagePreen_wide <-
ForagePreen_wide %>%
mutate(avg_flock_size_s = scale(avg_flock_size))%>%
mutate(flocksize_nearest_s = scale(flocksize_nearest))%>%
mutate(feedingperhour_s = scale(feedingperhour))Foraging models:
Foraging includes foraging on soil, in water, on human objects, and consuming human provided food.
Note: Focal follows were only conducted when people were not actively feeding the birds so foraging means probing on the ground for food. The few instances of consuming human provided food are cases where ibis were foraging ‘naturally’ and happened upon scraps of anthropogenic food that was already on the ground.
Exploratory Visualizations
Model selection:
Build a super model and then remove variables in a biologically relevant way to see how fit changes and compare AIC values. (set to ‘show nothing, run code’ so rmd isn’t super long)
Simple version:
#Simple model selection:
##No random effects:
#intercept only
summary(fmod0.3)## Family: nbinom2 ( log )
## Formula: Foraging ~ 1 + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1571.0 1580.1 -782.5 1565.0 147
##
##
## Dispersion parameter for nbinom2 family (): 0.987
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.91841 0.09627 -9.54 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0340 0.1881 -5.497 3.85e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning
fmod11 <-glmmTMB(Foraging~feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod11)## Family: nbinom2 ( log )
## Formula: Foraging ~ feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1567.9 1579.9 -779.9 1559.9 146
##
##
## Dispersion parameter for nbinom2 family (): 1.03
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.95398 0.09454 -10.091 <2e-16 ***
## feedingperhour_s -0.19827 0.08581 -2.311 0.0209 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0324 0.1878 -5.497 3.86e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#flock size
fmod12 <-glmmTMB(Foraging~flocksize_nearest_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod12)## Family: nbinom2 ( log )
## Formula: Foraging ~ flocksize_nearest_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1567.6 1579.6 -779.8 1559.6 146
##
##
## Dispersion parameter for nbinom2 family (): 1.03
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.94968 0.09438 -10.06 <2e-16 ***
## flocksize_nearest_s -0.26320 0.10240 -2.57 0.0102 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0343 0.1881 -5.5 3.8e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning + flock size
fmod13 <-glmmTMB(Foraging~flocksize_nearest_s+feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod13)## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s + feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1565.2 1580.3 -777.6 1555.2 145
##
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.97975 0.09296 -10.539 <2e-16 ***
## flocksize_nearest_s -0.24333 0.10301 -2.362 0.0182 *
## feedingperhour_s -0.18472 0.08670 -2.131 0.0331 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0330 0.1878 -5.499 3.82e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning x flock size
fmod14 <-glmmTMB(Foraging~flocksize_nearest_s*feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod14)## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s * feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1567.1 1585.2 -777.6 1555.1 144
##
##
## Dispersion parameter for nbinom2 family (): 1.07
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.97711 0.09345 -10.456 <2e-16 ***
## flocksize_nearest_s -0.24949 0.10501 -2.376 0.0175 *
## feedingperhour_s -0.20032 0.09952 -2.013 0.0441 *
## flocksize_nearest_s:feedingperhour_s -0.05511 0.17401 -0.317 0.7515
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0333 0.1879 -5.499 3.81e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AICtab(fmod0.3,fmod11,fmod12,fmod13,fmod14)## dAIC df
## fmod13 0.0 5
## fmod14 1.9 6
## fmod12 2.4 4
## fmod11 2.7 4
## fmod0.3 5.8 3##Same models but with site as random effect
#intercept only
summary(fmod0.2)## Family: nbinom2 ( log )
## Formula: Foraging ~ 1 + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1570.3 1582.4 -781.2 1562.3 146
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.08102 0.2846
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.05
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.9674 0.1599 -6.052 1.43e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.033 0.188 -5.498 3.84e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning
fmod15 <-glmmTMB(Foraging~feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod15)## Family: nbinom2 ( log )
## Formula:
## Foraging ~ feedingperhour_s + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1569.8 1584.9 -779.9 1559.8 145
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01202 0.1097
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.04
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.9640 0.1126 -8.561 <2e-16 ***
## feedingperhour_s -0.1861 0.1062 -1.752 0.0798 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0327 0.1879 -5.497 3.86e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#flock size
fmod16 <-glmmTMB(Foraging~flocksize_nearest_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod16)## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1569.6 1584.6 -779.8 1559.6 145
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 4.094e-07 0.0006398
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.03
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.94967 0.09439 -10.062 <2e-16 ***
## flocksize_nearest_s -0.26319 0.10244 -2.569 0.0102 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0343 0.1881 -5.5 3.8e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning + flock size
fmod17 <-glmmTMB(Foraging~flocksize_nearest_s+feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod17)## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s + feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1567.2 1585.3 -777.6 1555.2 144
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 2.283e-09 4.779e-05
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.97975 0.09296 -10.539 <2e-16 ***
## flocksize_nearest_s -0.24333 0.10301 -2.362 0.0182 *
## feedingperhour_s -0.18472 0.08670 -2.131 0.0331 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0330 0.1878 -5.499 3.82e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning x flock size
fmod18 <-glmmTMB(Foraging~flocksize_nearest_s*feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(fmod18)## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s * feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1569.1 1590.2 -777.6 1555.1 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 2.117e-09 4.601e-05
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.07
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.97710 0.09345 -10.455 <2e-16 ***
## flocksize_nearest_s -0.24949 0.10501 -2.376 0.0175 *
## feedingperhour_s -0.20032 0.09952 -2.013 0.0441 *
## flocksize_nearest_s:feedingperhour_s -0.05511 0.17401 -0.317 0.7515
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0333 0.1879 -5.499 3.81e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AICtab(fmod0.2,fmod15,fmod16,fmod17,fmod18) #fmod17 and fmod18 = best fit## dAIC df
## fmod17 0.0 6
## fmod18 1.9 7
## fmod16 2.4 5
## fmod15 2.6 5
## fmod0.2 3.1 4Pseudo R^{2} calculation
I think you could do this using the MuMIn package. It calculates conditional and marginal coefficient of determination for Generalized mixed-effect models. Marginal represents the variance explained by the fixed effects and conditional is interpreted as a variance explained by the entire model including both fixed and random effects.
library(MuMIn)##
## Attaching package: 'MuMIn'## The following object is masked from 'package:bbmle':
##
## AICcr.squaredGLMM(fmod17,fmod0.2) #warning: effects of zero-inflation and dispersion model are ignored ## Warning: 'r.squaredGLMM' now calculates a revised statistic. See the help page.## Warning in r.squaredGLMM.glmmTMB(fmod17, fmod0.2): the effects of zero-inflation
## and dispersion model are ignored## R2m R2c
## delta 0.028590314 0.028590314
## lognormal 0.063815282 0.063815284
## trigamma 0.007691387 0.007691387Ben Bolker also wrote a work-around for doing this directly. This can be accessed using the ‘performance’ add-on package (or using his crude code on github)
Link to discussion for future reference: https://github.com/glmmTMB/glmmTMB/issues/169
##THESE METHODS SOMEHOW DON'T ACCOUNT FOR RANDOM EFFECTS
performance::r2(fmod18)## Warning: Can't compute random effect variances. Some variance components equal
## zero. Your model may suffer from singularity (see `?lme4::isSingular`
## and `?performance::check_singularity`).
## Solution: Respecify random structure! You may also decrease the
## `tolerance` level to enforce the calculation of random effect variances.## Warning: mu of 0.4 is too close to zero, estimate of random effect variances may
## be unreliable.## Random effect variances not available. Returned R2 does not account for random effects.## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.008performance::r2_nakagawa(fmod17)## Warning: Can't compute random effect variances. Some variance components equal
## zero. Your model may suffer from singularity (see `?lme4::isSingular`
## and `?performance::check_singularity`).
## Solution: Respecify random structure! You may also decrease the
## `tolerance` level to enforce the calculation of random effect variances.
## Warning: mu of 0.4 is too close to zero, estimate of random effect variances may
## be unreliable.## Random effect variances not available. Returned R2 does not account for random effects.## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.008performance::model_performance(fmod18)## Random effect variances not available. Returned R2 does not account for random effects.## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | RMSE | Sigma | Score_log | Score_spherical
## --------------------------------------------------------------------------------------------------------
## 1569.121 | 1569.909 | 1590.195 | | 0.008 | 171.286 | 1.065 | -11.037 | 0.042performance::model_performance(fmod12)## Random effect variances not available. Returned R2 does not account for random effects.## # Indices of model performance
##
## AIC | AICc | BIC | R2 (cond.) | R2 (marg.) | RMSE | Sigma
## --------------------------------------------------------------------------
## 1567.594 | 1567.870 | 1579.636 | | 0.005 | 177.225 | 1.029performance::r2(fmod13)## Warning: mu of 0.4 is too close to zero, estimate of random effect variances may
## be unreliable.## Random effect variances not available. Returned R2 does not account for random effects.## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.008Hypothesis testing approach:
Is flock size important? Is provisioning important? (How important are they?) (set to ‘show nothing, run code’ so rmd isn’t super long)
Model diagnostics
Testing the fit of fmod17 and fmod18- the two best fitting models.
First test the fit of fmod17
## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s + feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1567.2 1585.3 -777.6 1555.2 144
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 2.283e-09 4.779e-05
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.97975 0.09296 -10.539 <2e-16 ***
## flocksize_nearest_s -0.24333 0.10301 -2.362 0.0182 *
## feedingperhour_s -0.18472 0.08670 -2.131 0.0331 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0330 0.1878 -5.499 3.82e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 0.65756, p-value = 0.148
## alternative hypothesis: two.sided
##
## DHARMa zero-inflation test via comparison to expected zeros with
## simulation under H0 = fitted model
##
## data: simulationOutput
## ratioObsSim = 1.0019, p-value = 1
## alternative hypothesis: two.sidedResiduals look fine. Plotting residuals against the two predictors suggests that there might be some issues for one of them.
Now test fit for fmod18
## Family: nbinom2 ( log )
## Formula:
## Foraging ~ flocksize_nearest_s * feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1569.1 1590.2 -777.6 1555.1 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 2.117e-09 4.601e-05
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.07
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.97710 0.09345 -10.455 <2e-16 ***
## flocksize_nearest_s -0.24949 0.10501 -2.376 0.0175 *
## feedingperhour_s -0.20032 0.09952 -2.013 0.0441 *
## flocksize_nearest_s:feedingperhour_s -0.05511 0.17401 -0.317 0.7515
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.0333 0.1879 -5.499 3.81e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 0.66608, p-value = 0.182
## alternative hypothesis: two.sided
##
## DHARMa zero-inflation test via comparison to expected zeros with
## simulation under H0 = fitted model
##
## data: simulationOutput
## ratioObsSim = 1.0021, p-value = 1
## alternative hypothesis: two.sidedThe residuals look pretty okay for this model too but there are more problems when I plot against specific predictors.
Preening models:
Preening includes preening or grooming.
Exploratory Visualizations
Model selection:
Build a super model and then remove variables in a biologically relevant way to see how fit changes and compare AIC values. (set to ‘show nothing, run code’ so rmd isn’t super long)
Simple version:
#Simple model selection:
##No random effects:
#intercept only
summary(pmod0.3)## Family: nbinom2 ( log )
## Formula: Preening ~ 1 + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1545.9 1554.9 -769.9 1539.9 147
##
##
## Dispersion parameter for nbinom2 family (): 0.763
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.158 0.108 -10.72 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1912 0.2037 -5.849 4.95e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning
pmod11 <-glmmTMB(Preening~feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod11)## Family: nbinom2 ( log )
## Formula: Preening ~ feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1547.2 1559.3 -769.6 1539.2 146
##
##
## Dispersion parameter for nbinom2 family (): 0.766
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.16616 0.10803 -10.795 <2e-16 ***
## feedingperhour_s 0.09753 0.12266 0.795 0.427
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1919 0.2038 -5.848 4.98e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#flock size
pmod12 <-glmmTMB(Preening~flocksize_nearest_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod12)## Family: nbinom2 ( log )
## Formula: Preening ~ flocksize_nearest_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1545.0 1557.0 -768.5 1537.0 146
##
##
## Dispersion parameter for nbinom2 family (): 0.783
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1765 0.1067 -11.022 <2e-16 ***
## flocksize_nearest_s 0.1638 0.1016 1.613 0.107
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1870 0.2027 -5.856 4.74e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning + flock size
pmod13 <-glmmTMB(Preening~flocksize_nearest_s+feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod13)## Family: nbinom2 ( log )
## Formula:
## Preening ~ flocksize_nearest_s + feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1546.6 1561.6 -768.3 1536.6 145
##
##
## Dispersion parameter for nbinom2 family (): 0.784
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.18239 0.10677 -11.074 <2e-16 ***
## flocksize_nearest_s 0.15642 0.10063 1.554 0.120
## feedingperhour_s 0.07797 0.11909 0.655 0.513
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1875 0.2028 -5.855 4.76e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning x flock size
pmod14 <-glmmTMB(Preening~flocksize_nearest_s*feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod14)## Family: nbinom2 ( log )
## Formula:
## Preening ~ flocksize_nearest_s * feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1548.6 1566.6 -768.3 1536.6 144
##
##
## Dispersion parameter for nbinom2 family (): 0.784
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.18402 0.10912 -10.851 <2e-16 ***
## flocksize_nearest_s 0.15785 0.10248 1.540 0.123
## feedingperhour_s 0.08129 0.12786 0.636 0.525
## flocksize_nearest_s:feedingperhour_s 0.01284 0.17902 0.072 0.943
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1877 0.2029 -5.855 4.77e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AICtab(pmod0.3,pmod11,pmod12,pmod13,pmod14)## dAIC df
## pmod12 0.0 4
## pmod0.3 0.9 3
## pmod13 1.6 5
## pmod11 2.2 4
## pmod14 3.6 6##Same models but with site as random effect
#intercept only
summary(pmod0.2)## Family: nbinom2 ( log )
## Formula: Preening ~ 1 + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1545.8 1557.8 -768.9 1537.8 146
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.07115 0.2667
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 0.802
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.2169 0.1624 -7.491 6.84e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1857 0.2025 -5.856 4.73e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning
pmod15 <-glmmTMB(Preening~feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod15)## Family: nbinom2 ( log )
## Formula:
## Preening ~ feedingperhour_s + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1547.7 1562.8 -768.9 1537.7 145
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.08273 0.2876
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 0.805
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.22063 0.17031 -7.167 7.65e-13 ***
## feedingperhour_s -0.03225 0.17501 -0.184 0.854
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1851 0.2023 -5.857 4.72e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#flock size
pmod16 <-glmmTMB(Preening~flocksize_nearest_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod16)## Family: nbinom2 ( log )
## Formula:
## Preening ~ flocksize_nearest_s + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1546.6 1561.7 -768.3 1536.6 145
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.03272 0.1809
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 0.799
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.2026 0.1384 -8.686 <2e-16 ***
## flocksize_nearest_s 0.1329 0.1219 1.091 0.275
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1848 0.2022 -5.858 4.68e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning + flock size
pmod17 <-glmmTMB(Preening~flocksize_nearest_s+feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod17)## Family: nbinom2 ( log )
## Formula:
## Preening ~ flocksize_nearest_s + feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1548.5 1566.6 -768.2 1536.5 144
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01502 0.1226
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 0.793
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.19393 0.12748 -9.366 <2e-16 ***
## flocksize_nearest_s 0.14585 0.11664 1.250 0.211
## feedingperhour_s 0.05801 0.15247 0.380 0.704
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1861 0.2026 -5.855 4.77e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning x flock size
pmod18 <-glmmTMB(Preening~flocksize_nearest_s*feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=ForagePreen_wide)
summary(pmod18)## Family: nbinom2 ( log )
## Formula:
## Preening ~ flocksize_nearest_s * feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: ForagePreen_wide
##
## AIC BIC logLik deviance df.resid
## 1550.5 1571.6 -768.2 1536.5 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01476 0.1215
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 0.792
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.194963 0.128629 -9.290 <2e-16 ***
## flocksize_nearest_s 0.147157 0.118857 1.238 0.216
## feedingperhour_s 0.060848 0.161153 0.378 0.706
## flocksize_nearest_s:feedingperhour_s 0.009679 0.179544 0.054 0.957
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1862 0.2026 -5.855 4.78e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AICtab(pmod0.2,pmod15,pmod16,pmod17,pmod18)## dAIC df
## pmod0.2 0.0 4
## pmod16 0.8 5
## pmod15 2.0 5
## pmod17 2.7 6
## pmod18 4.7 7The top performing models are within 2 AIC values of the intercept only null model.
Hypothesis testing approach:
Is flock size important? Is provisioning important? (How important are they?) (set to ‘show nothing, run code’ so rmd isn’t super long)
Model diagnostics
Not needed because the intercept only model is the best fitting model?
Vigilance models:
#library(mosaic) # standardizing variables
Vig_wide <-
Vig_wide %>%
mutate(avg_flock_size_s = scale(avg_flock_size))%>%
mutate(flocksize_nearest_s = scale(flocksize_nearest))%>%
mutate(feedingperhour_s = scale(feedingperhour))Exploratory Visualizations
Model selection:
Build a super model and then remove variables in a biologically relevant way to see how fit changes and compare AIC values. (set to ‘show nothing, run code’ so rmd isn’t super long)
Simple version:
#Simple model selection:
##No random effects:
#intercept only
summary(vmod0.3)## Family: nbinom2 ( log )
## Formula: Vigilant ~ 1 + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1795.1 1804.1 -894.5 1789.1 147
##
##
## Dispersion parameter for nbinom2 family (): 1.04
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1186 0.0831 -13.46 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7527 0.3674 -7.493 6.72e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning
vmod11 <-glmmTMB(Vigilant~feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod11)## Family: nbinom2 ( log )
## Formula: Vigilant ~ feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1795.2 1807.3 -893.6 1787.2 146
##
##
## Dispersion parameter for nbinom2 family (): 1.05
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.12883 0.08280 -13.634 <2e-16 ***
## feedingperhour_s 0.11559 0.08451 1.368 0.171
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7571 0.3691 -7.471 7.98e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#flock size
vmod12 <-glmmTMB(Vigilant~flocksize_nearest_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod12)## Family: nbinom2 ( log )
## Formula: Vigilant ~ flocksize_nearest_s + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1796.7 1808.7 -894.3 1788.7 146
##
##
## Dispersion parameter for nbinom2 family (): 1.05
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.11978 0.08298 -13.494 <2e-16 ***
## flocksize_nearest_s -0.05246 0.08319 -0.631 0.528
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7504 0.3665 -7.504 6.21e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning + flock size
vmod13 <-glmmTMB(Vigilant~flocksize_nearest_s+feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod13)## Family: nbinom2 ( log )
## Formula:
## Vigilant ~ flocksize_nearest_s + feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1796.6 1811.7 -893.3 1786.6 145
##
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.13097 0.08263 -13.688 <2e-16 ***
## flocksize_nearest_s -0.06498 0.08119 -0.800 0.423
## feedingperhour_s 0.12392 0.08560 1.448 0.148
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7546 0.3682 -7.482 7.33e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning x flock size
vmod14 <-glmmTMB(Vigilant~flocksize_nearest_s*feedingperhour_s+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod14)## Family: nbinom2 ( log )
## Formula:
## Vigilant ~ flocksize_nearest_s * feedingperhour_s + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1798.5 1816.6 -893.2 1786.5 144
##
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.13733 0.08423 -13.503 <2e-16 ***
## flocksize_nearest_s -0.05786 0.08320 -0.695 0.487
## feedingperhour_s 0.13835 0.09467 1.461 0.144
## flocksize_nearest_s:feedingperhour_s 0.05327 0.14684 0.363 0.717
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7558 0.3687 -7.474 7.75e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AICtab(vmod0.3,vmod11,vmod12,vmod13,vmod14)## dAIC df
## vmod0.3 0.0 3
## vmod11 0.2 4
## vmod13 1.5 5
## vmod12 1.6 4
## vmod14 3.4 6##Same models but with site as random effect
#intercept only
summary(vmod0.2)## Family: nbinom2 ( log )
## Formula: Vigilant ~ 1 + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1796.7 1808.8 -894.4 1788.7 146
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01613 0.127
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.1253 0.1008 -11.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7493 0.3662 -7.508 5.99e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning
vmod15 <-glmmTMB(Vigilant~feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod15)## Family: nbinom2 ( log )
## Formula:
## Vigilant ~ feedingperhour_s + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1796.9 1812.0 -893.5 1786.9 145
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.0167 0.1292
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.07
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.13354 0.10079 -11.247 <2e-16 ***
## feedingperhour_s 0.12838 0.09711 1.322 0.186
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7515 0.3671 -7.495 6.61e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#flock size
vmod16 <-glmmTMB(Vigilant~flocksize_nearest_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod16)## Family: nbinom2 ( log )
## Formula:
## Vigilant ~ flocksize_nearest_s + (1 | site) + offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1798.4 1813.4 -894.2 1788.4 145
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01607 0.1268
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.12738 0.10085 -11.18 <2e-16 ***
## flocksize_nearest_s -0.05547 0.09087 -0.61 0.542
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7480 0.3657 -7.514 5.73e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning + flock size
vmod17 <-glmmTMB(Vigilant~flocksize_nearest_s+feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod17)## Family: nbinom2 ( log )
## Formula:
## Vigilant ~ flocksize_nearest_s + feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1798.5 1816.6 -893.2 1786.5 144
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01066 0.1032
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.07
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.13444 0.09477 -11.971 <2e-16 ***
## flocksize_nearest_s -0.05885 0.08814 -0.668 0.504
## feedingperhour_s 0.12762 0.09276 1.376 0.169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7515 0.3671 -7.495 6.64e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#provisioning x flock size
vmod18 <-glmmTMB(Vigilant~flocksize_nearest_s*feedingperhour_s+(1|site)+offset(log(duration)),
family=nbinom2,
ziformula=~1,
data=Vig_wide)
summary(vmod18)## Family: nbinom2 ( log )
## Formula:
## Vigilant ~ flocksize_nearest_s * feedingperhour_s + (1 | site) +
## offset(log(duration))
## Zero inflation: ~1
## Data: Vig_wide
##
## AIC BIC logLik deviance df.resid
## 1800.4 1821.5 -893.2 1786.4 143
##
## Random effects:
##
## Conditional model:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.007085 0.08417
## Number of obs: 150, groups: site, 5
##
## Dispersion parameter for nbinom2 family (): 1.06
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.13790 0.09207 -12.359 <2e-16 ***
## flocksize_nearest_s -0.05544 0.08769 -0.632 0.527
## feedingperhour_s 0.13647 0.09856 1.385 0.166
## flocksize_nearest_s:feedingperhour_s 0.03804 0.16156 0.235 0.814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Zero-inflation model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.7533 0.3679 -7.483 7.24e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1AICtab(vmod0.2,vmod15,vmod16,vmod17,vmod18)## dAIC df
## vmod0.2 0.0 4
## vmod15 0.2 5
## vmod16 1.6 5
## vmod17 1.8 6
## vmod18 3.7 7The top performing models are within 2 AIC values of the intercept only null model.
Hypothesis testing approach:
Is flock size important? Is provisioning important? (How important are they?) (set to ‘show nothing, run code’ so rmd isn’t super long)
Model diagnostics
Not needed because the intercept only model is the best fitting model?